Antennas are part of some of the more critical components of a communication system, and in particular, wireless communication systems. In wireless communication systems, communication signals that are transmitted by antennas over traffic channels and signaling channels will at some point propagate through the air and be received by other antennas. Thus, part of or all of the medium of the traffic and signaling channels is the air itself. The traffic channels are communication channels through which users of the wireless communication system convey (i.e., transmit and/or receive) communication signals to each other. The communication signals typically carry information being conveyed between users. The signaling channels are communication channels through which signals that facilitate the control, maintenance and management of the communication system are conveyed. The signaling signals are typically transmitted by system equipment and user equipment. System equipment are various communication equipment owned, controlled and operated by a system operator or provider. Examples of system operators include local telephone companies and Internet service providers. User equipment are equipment that are typically owned and operated by users of the communication system. Examples of user equipment include cellular phones, wireless personal computers and pagers.
As the communication signals propagate through the air, they are adversely affected by various anomalies that distort such signals and cause part or all of the information being carried by said signals to be received erroneously. The quality of the communication channels can greatly affect the communication system's throughput. The throughput is the amount of information that is received without any errors for a given period of time. The various anomalies of a communication channel can adversely affect any one or all of a signal's parameters; some of these parameters include signal amplitude, signal phase, signal frequency. The signals are transmitted by transmit antennas and received by receive antennas. It should be noted that the antennas are often designed to operate as both transmit and receive antennas. To reduce the anomalous effects of a communication channel, communication systems often employ a feedback technique where a receive antenna transmits channel quality feedback information to a transmit antenna allowing the transmit antenna to modify, in some fashion, one or more of the signal's parameters. The channel quality feedback information is information about how transmitted signals are affected by the communication channel through which they have propagated. The signals propagating through the communication channel can therefore be manipulated so as to be less vulnerable to the various channel anomalies; thus the adverse effects of the channel are effectively reduced thus increasing throughput. Also, to increase system throughput, the communication system can use more than one transmit antenna and more than one receive antenna for the same or different signals.
Suppose, there are two transmit antennas and two receive antennas. The same information is transmitted by both transmit antennas. Although, the signals carry the same information, they may have different parameters. Therefore, the signals may be affected differently by the communication channel. Even when the signals carry the same information and have the same parameters, they may still be affected differently by the communication channel. One feedback technique used by many communication systems is to have the receive antennas transmit channel quality feedback information to the transmit antenna informing the transmit antennas about the quality of the transmitted signals. The parameters of the transmitted signal least adversely affected by the communication channel is then used in ensuing transmissions by the transmit antennas in an effort to improve the quality of the received signals.
Another technique is to pre-modify (or pre-process) the transmit signals based on the channel quality feedback information received by the transmit antennas from the receive antennas. The pre-modification (or pre-processing) compensates for the anomalies that the transmitted signals experience as they propagate through the communication channel. The channel quality feedback information may be based on measurements of previously transmitted signals or measurements of various channel parameters from signals transmitted over the signaling channel. A signal that is typically transmitted over the signaling channel and measured by the system is the pilot signal. Many wireless communication systems have a pilot signal that, among other purposes, serves to signal the presence of system equipment.
Yet, another technique is to measure the amount of energy contained in the two receive signals and send that information back to the transmit antennas. The parameters of the signal having the higher measured energy will be used for the next transmission. In all of the above feedback techniques, a rather brute force method is used to determine which set of signal parameters will allow a transmitted signal to be relatively less adversely affected by the communication channel. These brute force methods require a relatively large amount of information to be fed back to the transmit antennas. Further, the channel quality feedback information is continuously being sent back to the transmit antennas. Many communication systems have limited bandwidth for their signaling channels through which other critical information are conveyed. It may not, therefore, be practical to send all of the feedback information. Also, because the communication channel is a continually varying dynamic system, it may not be possible to efficiently and quickly modify the transmit signal to reduce its vulnerability to the channel anomalies.
Some communication systems attempt to characterize the communication channel mathematically so as to be able to develop more comprehensive channel quality feedback information that can sufficiently track the variations in the communication channel. For example, the communication channel can be modeled as an Eigenspace represented by an eigenvector matrix whose elements are complex numbers each of which is a basic unit that represents one or more measured parameters of the communication channel. The measured parameters of the channel include, for example, the effect of the channel on a signal's amplitude, the effect of the channel on a signal's phase and the effect of the channel on a signal's frequency. The measured channel parameters are also called channel parameters. For example suppose a signal is transmitted with an amplitude of 0 db, but such signal is received with a measured amplitude of −3 dB. The channel parameter for amplitude is thus −3 dB. When more than one transmitter and receiver are used, a channel parameter matrix can be generated from measured channel parameters.
A channel matrix can thus be formed from measurements of channel parameters. Again suppose, there are two transmit antennas (T1 and T2) and two receive antennas (R1 and R2). The channel parameter measurement at receive antenna R1 due to a signal transmitted by transmit antenna T1 is designated h11. The channel parameter measurement at receive antenna R2 due to a signal transmitted by transmit antenna T1 is designated h12. The channel parameter measurement at receive antenna R1 due to a signal transmitted by transmit antenna T2 is designated h21. The channel parameter measurement at receive antenna R2 due to a signal transmitted by transmit antenna T2 is designated h22. The measured channel parameters are elements of the channel matrix H, where:
  H  =      [                                        h            11                                                h            12                                                            h            21                                                h            22                                ]  and where h11,h12,h21, and h22 are complex numbers having complex conjugates h11*, h12*, h21* and h22*. A channel correlation matrix is obtained by performing a Hermitian operation on the channel matrix and pre-multiplying the channel matrix with this Hermitian matrix. The Hermitian operation is a well known matrix mathematical conversion in which all of the elements of the matrix are changed to their complex conjugates and the transpose of the complex conjugate matrix is performed. Thus the Hermitian matrix of channel matrix H is H+ where H+=[H*]T. The channel correlation matrix is designated as S where S≡H+H.
The elements of the channel correlation matrix, S, are related to eigenvalues and eigenvectors which can be obtained by a well known procedure called an eigenvalue decomposition, Applied Linear Algebra, 2d edition, Ben Noble, James W. Daniel, Prentice Hall Inc., 1977 and 1969, ISBN 0-13-041343-7. First it is recognized that S=ΣΛΣ+ where Σ is the eigenvector matrix. Σ is a unitary matrix meaning that Σ+Σ=ΣΣ+=I where I is an identity matrix. Λ is a diagonal eigenvalue matrix whose elements are eigenvalues and Σ is a matrix whose columns are eigenvectors or equivalently eigenbeams. For a 2×2 system (i.e., two transmit antennas and two receive antennas):
  Λ  =      [                                        λ            1                                    0                                      0                                      λ            2                                ]  where elements λ1 and λ2 are the eigenvalues; and Σ=[e1 e2] where e1 and e2 are eigenvectors which are the columns of the eigenvector matrix. Also, for a 2×2 system,
  I  =            [                                    1                                0                                                0                                1                              ]        .  Because S is known and I is a known constant matrix, the eigenvalues (i.e., λ) are obtained by solving the following equation:det[S−λI]=0where det represents the determinant operation. The values for Σ are then obtained by solving the equation Se=λe; i.e., because S is known and λ is known, e can be determined. Once the eigenvectors are obtained, channel quality feedback information—represented in terms of the eigenvectors—is sent or fed back to the transmit antennas to allow these antennas to modify the transmit signals so as to reduce the distortion experienced by these signals.
The channel quality feedback information in the form of eigenvalues and/or eigenvectors represents a relatively large amount of information that is to be periodically transmitted over band-limited signaling channels of the communication system. Further, many times some of the channel information being transmitted in the form of eigenvalues and/or eigenvectors are not as accurate in their characterization of the communication channel. In other words, there are certain eigenvalues that more accurately represent the communication channel characteristics than other eigenvalues.
In a single-transmit-single-receive antenna system, the transmission power can be determined using the well known procedure called the water-filling approach. However, for a multiple-transmit-multiple-receive antenna system, this method will not work simply because the channels between different antennas are interfering with each other. In this case, it is usually assumed that the same transmit power is given for each eigenbeam. Artificial ways of providing different transmit power to different eigenbeams is possible but this involves experimental fine tuning to determined the amount of power should be given and is usually not very effective.